write the equation of a line parallel to the given line but passing through the given point problem y=1/2 x +1; (4,2)

Question

y=1/2 x+1; (4,2)

Answer 1

A formula for a line may be:
       Ax + By = C                       in Standard form
       y = mx + b                        in slope-intercept form
       y – y₁ = m(x – x₁)             in point-slope form
  etc.

A parallel line has the same slope, but a different y-intercept or passes through a different point or …

Also (for info), a perpendicular line has a slope that is the negative reciprocal of the slope of the given line and has a different y-intercept or passes through a different point or …

That means that you should make a table of (1) formula for a line, (2) the formula for a parallel line, (3) the formula for a perpendicular line, …   using each of the three equations above.  Books and classes will teach you one of these at a time, but you will see problems on standardized tests that assume that you can do any of them as needed.   Add to your table as you learn new information.

O.K., this problem seeks a parallel line passing through a given point.  Your entry in a “review table” would show: 

     Equation of line         parallel line through a point        perpendicular line through a point  …

      slope-intercept form
        y = mx + b                     y =  mx  + b₁                            etc.

      etc.

 The slope of the new line is the same as the slope of the given line (m=1/2).  The new y-intercept is found by putting the values of x and y into the formula and finding b₁.  So, 
     2 = (1/2)4 + b₁
    b₁ = 0                (subtract 2 from both sides; switch sides)

The equation of the parallel line is:    y = (1/2)x

Checking:
  Is the line y = (1/2)x   parallel to the line y = (1/2)x + 1 ?       yes (same slope)
  Does the line y = (1/2)x  pass through the point (4,2)  ?
      Re-written:  Is   2 = (1/2)4   ?   yes